Hi，The usage of "宅在家里" comes from Japan, which is not an authentic Chinese language. It's just a kind of network language. Generally speaking, “呆在家里” is a common use to express "staying at home", so you can use it. “宅在家里” and “呆在家里” have simillar meaning, but “宅在家里” is more used to describe a person who doesn't want to go out and just staying at home playing games and sleeping, or is very lazy. In short, “宅在家里” has a sense of humor and peole who use it tend to make some harmless jokes, but “呆在家里” doesn't have that kind of banter.

呆and宅，At the level of Chinese characters.It means the same thing.=stay. stay at home. ’宅’come form japan,otaku culture,Close to a state of self-containment. but now in china,between呆and宅,No concrete difference.

Hi, There aren't much semantic differences between these two expressions. But there is a little nuance there. Basically people who say '我宅在家里‘ prefer to stay at home than go outside when he or she is free to some extent. However, '我呆在家里’simply means the speaker is not going anywhere. Hopefully my answer will be helpful to you .Good luck !